Television viewing reached a new high when the Nielsen Company reported a mean d

Question

Television viewing reached a new high when the Nielsen Company reported a mean daily viewing time of 8.35 hours per household (USA Today, November 11, 2009). Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household.

A) What is the probability that a household views television between 5 and 10 hours a day?

B) How many hours of television viewing must a household have in order to be in the top 3% of all television viewing households?

C) What is the probability that a household views television more than 3 hours a day?

Explanation / Answer

Mean is 8.35 and standard deviation is 2.5

A) P(5<X<10) =P((5-8.35)/2.5<z<(10-8.35)/2.5) =P(-1.34<z<0.66)=P(z<0.66)-P(z<-1.34)=P(z<0.66)-(1-P(z<1.34))

From normal distibution table, this is 0.7454-(1-0.9099)= 0.6553

B) Top 3% means the top value in bottom 97%. for 0.97 , the z value is 1.88

thus (x-8.35)/2.5=1.88 or x=1.88*2.5+8.35=13.05

C)P(X>3)=P(z>(3-8.35)/2.5) =P(z>-2.14)=P(z<2.14)

from normal table it is 0.9838

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